%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN254-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:38:36 AM UTC 2025
% Result : Unsatisfiable 0.48s 0.64s
% Output : Proof 0.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYN254-1 : TPTP v9.0.0. Released v1.1.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n006.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 12:29:35 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.48/0.64 % SZS status Unsatisfiable
% 0.48/0.64 % SZS output start Proof
% 0.48/0.64 tff(q2_type, type, (
% 0.48/0.64 q2: ( $i * $i * $i ) > $o)).
% 0.48/0.64 tff(b_type, type, (
% 0.48/0.64 b: $i)).
% 0.48/0.64 tff(a_type, type, (
% 0.48/0.64 a: $i)).
% 0.48/0.64 tff(s1_type, type, (
% 0.48/0.64 s1: $i > $o)).
% 0.48/0.64 tff(p0_type, type, (
% 0.48/0.64 p0: ( $i * $i ) > $o)).
% 0.48/0.64 tff(s2_type, type, (
% 0.48/0.64 s2: $i > $o)).
% 0.48/0.64 tff(s3_type, type, (
% 0.48/0.64 s3: ( $i * $i ) > $o)).
% 0.48/0.64 tff(e_type, type, (
% 0.48/0.64 e: $i)).
% 0.48/0.64 tff(l2_type, type, (
% 0.48/0.64 l2: ( $i * $i ) > $o)).
% 0.48/0.64 tff(m1_type, type, (
% 0.48/0.64 m1: ( $i * $i * $i ) > $o)).
% 0.48/0.64 tff(m0_type, type, (
% 0.48/0.64 m0: ( $i * $i * $i ) > $o)).
% 0.48/0.64 tff(l0_type, type, (
% 0.48/0.64 l0: $i > $o)).
% 0.48/0.64 tff(m4_type, type, (
% 0.48/0.64 m4: ( $i * $i ) > $o)).
% 0.48/0.64 tff(p1_type, type, (
% 0.48/0.64 p1: ( $i * $i * $i ) > $o)).
% 0.48/0.64 tff(n1_type, type, (
% 0.48/0.64 n1: ( $i * $i * $i ) > $o)).
% 0.48/0.64 tff(s0_type, type, (
% 0.48/0.64 s0: $i > $o)).
% 0.48/0.64 tff(l1_type, type, (
% 0.48/0.64 l1: ( $i * $i ) > $o)).
% 0.48/0.64 tff(n0_type, type, (
% 0.48/0.64 n0: ( $i * $i ) > $o)).
% 0.48/0.64 tff(c_type, type, (
% 0.48/0.64 c: $i)).
% 0.48/0.64 tff(k0_type, type, (
% 0.48/0.64 k0: $i > $o)).
% 0.48/0.64 tff(1,assumption,(~p0(b, b)), introduced(assumption)).
% 0.48/0.64 tff(2,plain,
% 0.48/0.64 (^[X: $i] : refl(p0(b, X) <=> p0(b, X))),
% 0.48/0.64 inference(bind,[status(th)],[])).
% 0.48/0.64 tff(3,plain,
% 0.48/0.64 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.48/0.64 inference(quant_intro,[status(thm)],[2])).
% 0.48/0.64 tff(4,plain,
% 0.48/0.64 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(5,axiom,(![X: $i] : p0(b, X)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_14')).
% 0.48/0.64 tff(6,plain,
% 0.48/0.64 (![X: $i] : p0(b, X)),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.48/0.64 tff(7,plain,(
% 0.48/0.64 ![X: $i] : p0(b, X)),
% 0.48/0.64 inference(skolemize,[status(sab)],[6])).
% 0.48/0.64 tff(8,plain,
% 0.48/0.64 (![X: $i] : p0(b, X)),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.48/0.64 tff(9,plain,
% 0.48/0.64 ((~![X: $i] : p0(b, X)) | p0(b, b)),
% 0.48/0.64 inference(quant_inst,[status(thm)],[])).
% 0.48/0.64 tff(10,plain,
% 0.48/0.64 ($false),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.48/0.64 tff(11,plain,(p0(b, b)), inference(lemma,lemma(discharge,[]))).
% 0.48/0.64 tff(12,plain,
% 0.48/0.64 (^[I: $i] : refl((s1(I) | (~p0(I, I))) <=> (s1(I) | (~p0(I, I))))),
% 0.48/0.64 inference(bind,[status(th)],[])).
% 0.48/0.64 tff(13,plain,
% 0.48/0.64 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.48/0.64 inference(quant_intro,[status(thm)],[12])).
% 0.48/0.64 tff(14,plain,
% 0.48/0.64 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(15,axiom,(![I: $i] : (s1(I) | (~p0(I, I)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_125')).
% 0.48/0.64 tff(16,plain,
% 0.48/0.64 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.48/0.64 tff(17,plain,(
% 0.48/0.64 ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.48/0.64 inference(skolemize,[status(sab)],[16])).
% 0.48/0.64 tff(18,plain,
% 0.48/0.64 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.48/0.64 tff(19,plain,
% 0.48/0.64 (((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))) <=> ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b)))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(20,plain,
% 0.48/0.64 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))),
% 0.48/0.64 inference(quant_inst,[status(thm)],[])).
% 0.48/0.64 tff(21,plain,
% 0.48/0.64 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.48/0.64 tff(22,plain,
% 0.48/0.64 (s1(b)),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[21, 18, 11])).
% 0.48/0.64 tff(23,plain,
% 0.48/0.64 (^[B: $i, D: $i, C: $i] : refl(((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C)) <=> ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C)))),
% 0.48/0.64 inference(bind,[status(th)],[])).
% 0.48/0.64 tff(24,plain,
% 0.48/0.64 (![B: $i, D: $i, C: $i] : ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C)) <=> ![B: $i, D: $i, C: $i] : ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C))),
% 0.48/0.64 inference(quant_intro,[status(thm)],[23])).
% 0.48/0.64 tff(25,plain,
% 0.48/0.64 (![B: $i, D: $i, C: $i] : ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C)) <=> ![B: $i, D: $i, C: $i] : ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(26,plain,
% 0.48/0.64 (^[B: $i, D: $i, C: $i] : trans(monotonicity(rewrite((m1(B, C, C) | (~l0(D))) <=> ((~l0(D)) | m1(B, C, C))), (((m1(B, C, C) | (~l0(D))) | (~m0(C, C, B))) <=> (((~l0(D)) | m1(B, C, C)) | (~m0(C, C, B))))), rewrite((((~l0(D)) | m1(B, C, C)) | (~m0(C, C, B))) <=> ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C))), (((m1(B, C, C) | (~l0(D))) | (~m0(C, C, B))) <=> ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C))))),
% 0.48/0.64 inference(bind,[status(th)],[])).
% 0.48/0.64 tff(27,plain,
% 0.48/0.64 (![B: $i, D: $i, C: $i] : ((m1(B, C, C) | (~l0(D))) | (~m0(C, C, B))) <=> ![B: $i, D: $i, C: $i] : ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C))),
% 0.48/0.64 inference(quant_intro,[status(thm)],[26])).
% 0.48/0.64 tff(28,axiom,(![B: $i, D: $i, C: $i] : ((m1(B, C, C) | (~l0(D))) | (~m0(C, C, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_015')).
% 0.48/0.64 tff(29,plain,
% 0.48/0.64 (![B: $i, D: $i, C: $i] : ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.48/0.64 tff(30,plain,
% 0.48/0.64 (![B: $i, D: $i, C: $i] : ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.48/0.64 tff(31,plain,(
% 0.48/0.64 ![B: $i, D: $i, C: $i] : ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C))),
% 0.48/0.64 inference(skolemize,[status(sab)],[30])).
% 0.48/0.64 tff(32,plain,
% 0.48/0.64 (![B: $i, D: $i, C: $i] : ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.48/0.64 tff(33,plain,
% 0.48/0.64 (m0(b, b, e) <=> m0(b, b, e)),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(34,axiom,(m0(b, b, e)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_31')).
% 0.48/0.64 tff(35,plain,
% 0.48/0.64 (m0(b, b, e)),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.48/0.64 tff(36,plain,
% 0.48/0.64 (l0(a) <=> l0(a)),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(37,axiom,(l0(a)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_20')).
% 0.48/0.64 tff(38,plain,
% 0.48/0.64 (l0(a)),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.48/0.64 tff(39,plain,
% 0.48/0.64 (((~![B: $i, D: $i, C: $i] : ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C))) | ((~l0(a)) | (~m0(b, b, e)) | m1(e, b, b))) <=> ((~![B: $i, D: $i, C: $i] : ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C))) | (~l0(a)) | (~m0(b, b, e)) | m1(e, b, b))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(40,plain,
% 0.48/0.64 ((~![B: $i, D: $i, C: $i] : ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C))) | ((~l0(a)) | (~m0(b, b, e)) | m1(e, b, b))),
% 0.48/0.64 inference(quant_inst,[status(thm)],[])).
% 0.48/0.64 tff(41,plain,
% 0.48/0.64 ((~![B: $i, D: $i, C: $i] : ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C))) | (~l0(a)) | (~m0(b, b, e)) | m1(e, b, b)),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.48/0.64 tff(42,plain,
% 0.48/0.64 (m1(e, b, b)),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[41, 38, 35, 32])).
% 0.48/0.64 tff(43,plain,
% 0.48/0.64 (^[I: $i, H: $i, G: $i] : refl(((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H))) <=> ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H))))),
% 0.48/0.64 inference(bind,[status(th)],[])).
% 0.48/0.64 tff(44,plain,
% 0.48/0.64 (![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H))) <=> ![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))),
% 0.48/0.64 inference(quant_intro,[status(thm)],[43])).
% 0.48/0.64 tff(45,plain,
% 0.48/0.64 (![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H))) <=> ![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(46,plain,
% 0.48/0.64 (^[I: $i, H: $i, G: $i] : trans(monotonicity(trans(monotonicity(rewrite((l2(G, G) | (~m0(H, G, I))) <=> ((~m0(H, G, I)) | l2(G, G))), (((l2(G, G) | (~m0(H, G, I))) | (~m1(I, H, H))) <=> (((~m0(H, G, I)) | l2(G, G)) | (~m1(I, H, H))))), rewrite((((~m0(H, G, I)) | l2(G, G)) | (~m1(I, H, H))) <=> ((~m0(H, G, I)) | l2(G, G) | (~m1(I, H, H)))), (((l2(G, G) | (~m0(H, G, I))) | (~m1(I, H, H))) <=> ((~m0(H, G, I)) | l2(G, G) | (~m1(I, H, H))))), ((((l2(G, G) | (~m0(H, G, I))) | (~m1(I, H, H))) | (~p0(H, G))) <=> (((~m0(H, G, I)) | l2(G, G) | (~m1(I, H, H))) | (~p0(H, G))))), rewrite((((~m0(H, G, I)) | l2(G, G) | (~m1(I, H, H))) | (~p0(H, G))) <=> ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))), ((((l2(G, G) | (~m0(H, G, I))) | (~m1(I, H, H))) | (~p0(H, G))) <=> ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))))),
% 0.48/0.64 inference(bind,[status(th)],[])).
% 0.48/0.64 tff(47,plain,
% 0.48/0.64 (![I: $i, H: $i, G: $i] : (((l2(G, G) | (~m0(H, G, I))) | (~m1(I, H, H))) | (~p0(H, G))) <=> ![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))),
% 0.48/0.65 inference(quant_intro,[status(thm)],[46])).
% 0.48/0.65 tff(48,axiom,(![I: $i, H: $i, G: $i] : (((l2(G, G) | (~m0(H, G, I))) | (~m1(I, H, H))) | (~p0(H, G)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_134')).
% 0.48/0.65 tff(49,plain,
% 0.48/0.65 (![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.48/0.65 tff(50,plain,
% 0.48/0.65 (![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.48/0.65 tff(51,plain,(
% 0.48/0.65 ![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))),
% 0.48/0.65 inference(skolemize,[status(sab)],[50])).
% 0.48/0.65 tff(52,plain,
% 0.48/0.65 (![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.48/0.65 tff(53,plain,
% 0.48/0.65 (((~![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))) | (l2(b, b) | (~m0(b, b, e)) | (~p0(b, b)) | (~m1(e, b, b)))) <=> ((~![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))) | l2(b, b) | (~m0(b, b, e)) | (~p0(b, b)) | (~m1(e, b, b)))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(54,plain,
% 0.48/0.65 (((~m0(b, b, e)) | (~p0(b, b)) | l2(b, b) | (~m1(e, b, b))) <=> (l2(b, b) | (~m0(b, b, e)) | (~p0(b, b)) | (~m1(e, b, b)))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(55,plain,
% 0.48/0.65 (((~![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))) | ((~m0(b, b, e)) | (~p0(b, b)) | l2(b, b) | (~m1(e, b, b)))) <=> ((~![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))) | (l2(b, b) | (~m0(b, b, e)) | (~p0(b, b)) | (~m1(e, b, b))))),
% 0.48/0.65 inference(monotonicity,[status(thm)],[54])).
% 0.48/0.65 tff(56,plain,
% 0.48/0.65 (((~![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))) | ((~m0(b, b, e)) | (~p0(b, b)) | l2(b, b) | (~m1(e, b, b)))) <=> ((~![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))) | l2(b, b) | (~m0(b, b, e)) | (~p0(b, b)) | (~m1(e, b, b)))),
% 0.48/0.65 inference(transitivity,[status(thm)],[55, 53])).
% 0.48/0.65 tff(57,plain,
% 0.48/0.65 ((~![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))) | ((~m0(b, b, e)) | (~p0(b, b)) | l2(b, b) | (~m1(e, b, b)))),
% 0.48/0.65 inference(quant_inst,[status(thm)],[])).
% 0.48/0.65 tff(58,plain,
% 0.48/0.65 ((~![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))) | l2(b, b) | (~m0(b, b, e)) | (~p0(b, b)) | (~m1(e, b, b))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.48/0.65 tff(59,plain,
% 0.48/0.65 (l2(b, b) | (~p0(b, b)) | (~m1(e, b, b))),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[58, 35, 52])).
% 0.48/0.65 tff(60,plain,
% 0.48/0.65 (l2(b, b) | (~p0(b, b))),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[59, 42])).
% 0.48/0.65 tff(61,plain,
% 0.48/0.65 (l2(b, b)),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[60, 11])).
% 0.48/0.65 tff(62,plain,
% 0.48/0.65 ((~m4(e, b)) <=> (~m4(e, b))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(63,axiom,(~m4(e, b)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.48/0.65 tff(64,plain,
% 0.48/0.65 (~m4(e, b)),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.48/0.65 tff(65,plain,
% 0.48/0.65 (^[E: $i, F: $i, G: $i] : refl(((~l2(G, F)) | (~s3(a, E)) | m4(E, F)) <=> ((~l2(G, F)) | (~s3(a, E)) | m4(E, F)))),
% 0.48/0.65 inference(bind,[status(th)],[])).
% 0.48/0.65 tff(66,plain,
% 0.48/0.65 (![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F)) <=> ![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))),
% 0.48/0.65 inference(quant_intro,[status(thm)],[65])).
% 0.48/0.65 tff(67,plain,
% 0.48/0.65 (![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F)) <=> ![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(68,plain,
% 0.48/0.65 (^[E: $i, F: $i, G: $i] : trans(monotonicity(rewrite((m4(E, F) | (~l2(G, F))) <=> ((~l2(G, F)) | m4(E, F))), (((m4(E, F) | (~l2(G, F))) | (~s3(a, E))) <=> (((~l2(G, F)) | m4(E, F)) | (~s3(a, E))))), rewrite((((~l2(G, F)) | m4(E, F)) | (~s3(a, E))) <=> ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))), (((m4(E, F) | (~l2(G, F))) | (~s3(a, E))) <=> ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))))),
% 0.48/0.65 inference(bind,[status(th)],[])).
% 0.48/0.65 tff(69,plain,
% 0.48/0.65 (![E: $i, F: $i, G: $i] : ((m4(E, F) | (~l2(G, F))) | (~s3(a, E))) <=> ![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))),
% 0.48/0.65 inference(quant_intro,[status(thm)],[68])).
% 0.48/0.65 tff(70,axiom,(![E: $i, F: $i, G: $i] : ((m4(E, F) | (~l2(G, F))) | (~s3(a, E)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_279')).
% 0.48/0.65 tff(71,plain,
% 0.48/0.65 (![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.48/0.65 tff(72,plain,
% 0.48/0.65 (![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.48/0.65 tff(73,plain,(
% 0.48/0.65 ![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))),
% 0.48/0.65 inference(skolemize,[status(sab)],[72])).
% 0.48/0.65 tff(74,plain,
% 0.48/0.65 (![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))),
% 0.50/0.65 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.50/0.65 tff(75,plain,
% 0.50/0.65 (((~![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))) | ((~l2(b, b)) | (~s3(a, e)) | m4(e, b))) <=> ((~![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))) | (~l2(b, b)) | (~s3(a, e)) | m4(e, b))),
% 0.50/0.65 inference(rewrite,[status(thm)],[])).
% 0.50/0.65 tff(76,plain,
% 0.50/0.65 ((~![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))) | ((~l2(b, b)) | (~s3(a, e)) | m4(e, b))),
% 0.50/0.65 inference(quant_inst,[status(thm)],[])).
% 0.50/0.65 tff(77,plain,
% 0.50/0.65 ((~![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))) | (~l2(b, b)) | (~s3(a, e)) | m4(e, b)),
% 0.50/0.65 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.50/0.65 tff(78,plain,
% 0.50/0.65 (~s3(a, e)),
% 0.50/0.65 inference(unit_resolution,[status(thm)],[77, 74, 64, 61])).
% 0.50/0.65 tff(79,plain,
% 0.50/0.65 (^[I: $i] : refl((q2(I, I, I) | (~p1(I, I, I))) <=> (q2(I, I, I) | (~p1(I, I, I))))),
% 0.50/0.65 inference(bind,[status(th)],[])).
% 0.50/0.65 tff(80,plain,
% 0.50/0.65 (![I: $i] : (q2(I, I, I) | (~p1(I, I, I))) <=> ![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 0.50/0.65 inference(quant_intro,[status(thm)],[79])).
% 0.50/0.65 tff(81,plain,
% 0.50/0.65 (![I: $i] : (q2(I, I, I) | (~p1(I, I, I))) <=> ![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 0.50/0.65 inference(rewrite,[status(thm)],[])).
% 0.50/0.65 tff(82,axiom,(![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_181')).
% 0.50/0.65 tff(83,plain,
% 0.50/0.65 (![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 0.50/0.65 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.50/0.65 tff(84,plain,(
% 0.50/0.65 ![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 0.50/0.65 inference(skolemize,[status(sab)],[83])).
% 0.50/0.65 tff(85,plain,
% 0.50/0.65 (![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 0.50/0.65 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.50/0.65 tff(86,plain,
% 0.50/0.65 (((~l0(a)) | p1(a, a, a)) <=> ((~l0(a)) | p1(a, a, a))),
% 0.50/0.65 inference(rewrite,[status(thm)],[])).
% 0.50/0.65 tff(87,plain,
% 0.50/0.65 ((p1(a, a, a) | (~l0(a))) <=> ((~l0(a)) | p1(a, a, a))),
% 0.50/0.65 inference(rewrite,[status(thm)],[])).
% 0.50/0.65 tff(88,axiom,(p1(a, a, a) | (~l0(a))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_088')).
% 0.50/0.65 tff(89,plain,
% 0.50/0.65 ((~l0(a)) | p1(a, a, a)),
% 0.50/0.65 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.50/0.65 tff(90,plain,
% 0.50/0.65 ((~l0(a)) | p1(a, a, a)),
% 0.50/0.65 inference(modus_ponens,[status(thm)],[89, 86])).
% 0.50/0.65 tff(91,plain,
% 0.50/0.65 (p1(a, a, a)),
% 0.50/0.65 inference(unit_resolution,[status(thm)],[90, 38])).
% 0.50/0.65 tff(92,plain,
% 0.50/0.65 (((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | ((~p1(a, a, a)) | q2(a, a, a))) <=> ((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (~p1(a, a, a)) | q2(a, a, a))),
% 0.50/0.65 inference(rewrite,[status(thm)],[])).
% 0.50/0.65 tff(93,plain,
% 0.50/0.65 ((q2(a, a, a) | (~p1(a, a, a))) <=> ((~p1(a, a, a)) | q2(a, a, a))),
% 0.50/0.65 inference(rewrite,[status(thm)],[])).
% 0.50/0.65 tff(94,plain,
% 0.50/0.65 (((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (q2(a, a, a) | (~p1(a, a, a)))) <=> ((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | ((~p1(a, a, a)) | q2(a, a, a)))),
% 0.50/0.65 inference(monotonicity,[status(thm)],[93])).
% 0.50/0.65 tff(95,plain,
% 0.50/0.65 (((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (q2(a, a, a) | (~p1(a, a, a)))) <=> ((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (~p1(a, a, a)) | q2(a, a, a))),
% 0.50/0.65 inference(transitivity,[status(thm)],[94, 92])).
% 0.50/0.65 tff(96,plain,
% 0.50/0.65 ((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (q2(a, a, a) | (~p1(a, a, a)))),
% 0.50/0.65 inference(quant_inst,[status(thm)],[])).
% 0.50/0.65 tff(97,plain,
% 0.50/0.65 ((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (~p1(a, a, a)) | q2(a, a, a)),
% 0.50/0.65 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.50/0.65 tff(98,plain,
% 0.50/0.65 (q2(a, a, a)),
% 0.50/0.65 inference(unit_resolution,[status(thm)],[97, 91, 85])).
% 0.50/0.65 tff(99,plain,
% 0.50/0.65 (^[I: $i, B: $i, A: $i, J: $i] : refl(((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J)) <=> ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J)))),
% 0.50/0.65 inference(bind,[status(th)],[])).
% 0.50/0.65 tff(100,plain,
% 0.50/0.65 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J)) <=> ![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.50/0.65 inference(quant_intro,[status(thm)],[99])).
% 0.50/0.65 tff(101,plain,
% 0.50/0.65 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J)) <=> ![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.50/0.65 inference(rewrite,[status(thm)],[])).
% 0.50/0.65 tff(102,plain,
% 0.50/0.65 (^[I: $i, B: $i, A: $i, J: $i] : trans(monotonicity(trans(monotonicity(rewrite((s3(I, J) | (~q2(A, I, A))) <=> ((~q2(A, I, A)) | s3(I, J))), (((s3(I, J) | (~q2(A, I, A))) | (~s2(I))) <=> (((~q2(A, I, A)) | s3(I, J)) | (~s2(I))))), rewrite((((~q2(A, I, A)) | s3(I, J)) | (~s2(I))) <=> ((~s2(I)) | (~q2(A, I, A)) | s3(I, J))), (((s3(I, J) | (~q2(A, I, A))) | (~s2(I))) <=> ((~s2(I)) | (~q2(A, I, A)) | s3(I, J)))), ((((s3(I, J) | (~q2(A, I, A))) | (~s2(I))) | (~m0(A, B, J))) <=> (((~s2(I)) | (~q2(A, I, A)) | s3(I, J)) | (~m0(A, B, J))))), rewrite((((~s2(I)) | (~q2(A, I, A)) | s3(I, J)) | (~m0(A, B, J))) <=> ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))), ((((s3(I, J) | (~q2(A, I, A))) | (~s2(I))) | (~m0(A, B, J))) <=> ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))))),
% 0.50/0.65 inference(bind,[status(th)],[])).
% 0.50/0.65 tff(103,plain,
% 0.50/0.65 (![I: $i, B: $i, A: $i, J: $i] : (((s3(I, J) | (~q2(A, I, A))) | (~s2(I))) | (~m0(A, B, J))) <=> ![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.50/0.65 inference(quant_intro,[status(thm)],[102])).
% 0.50/0.65 tff(104,axiom,(![I: $i, B: $i, A: $i, J: $i] : (((s3(I, J) | (~q2(A, I, A))) | (~s2(I))) | (~m0(A, B, J)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_273')).
% 0.50/0.65 tff(105,plain,
% 0.50/0.65 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.50/0.65 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.50/0.65 tff(106,plain,
% 0.50/0.65 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.50/0.65 inference(modus_ponens,[status(thm)],[105, 101])).
% 0.50/0.65 tff(107,plain,(
% 0.50/0.65 ![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.50/0.65 inference(skolemize,[status(sab)],[106])).
% 0.50/0.65 tff(108,plain,
% 0.50/0.65 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.50/0.65 inference(modus_ponens,[status(thm)],[107, 100])).
% 0.50/0.65 tff(109,plain,
% 0.50/0.65 (m0(a, e, e) <=> m0(a, e, e)),
% 0.50/0.65 inference(rewrite,[status(thm)],[])).
% 0.50/0.65 tff(110,axiom,(m0(a, e, e)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_23')).
% 0.50/0.65 tff(111,plain,
% 0.50/0.65 (m0(a, e, e)),
% 0.50/0.65 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.50/0.65 tff(112,plain,
% 0.50/0.65 (((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | ((~s2(a)) | (~m0(a, e, e)) | (~q2(a, a, a)) | s3(a, e))) <=> ((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | (~s2(a)) | (~m0(a, e, e)) | (~q2(a, a, a)) | s3(a, e))),
% 0.50/0.65 inference(rewrite,[status(thm)],[])).
% 0.50/0.65 tff(113,plain,
% 0.50/0.65 ((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | ((~s2(a)) | (~m0(a, e, e)) | (~q2(a, a, a)) | s3(a, e))),
% 0.50/0.65 inference(quant_inst,[status(thm)],[])).
% 0.50/0.65 tff(114,plain,
% 0.50/0.65 ((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | (~s2(a)) | (~m0(a, e, e)) | (~q2(a, a, a)) | s3(a, e)),
% 0.50/0.65 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.50/0.65 tff(115,plain,
% 0.50/0.65 (~s2(a)),
% 0.50/0.65 inference(unit_resolution,[status(thm)],[114, 111, 108, 98, 78])).
% 0.50/0.65 tff(116,plain,
% 0.50/0.65 (^[H: $i] : refl(((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ((~s1(b)) | s2(H) | (~q2(b, H, b))))),
% 0.50/0.65 inference(bind,[status(th)],[])).
% 0.50/0.65 tff(117,plain,
% 0.50/0.65 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.50/0.65 inference(quant_intro,[status(thm)],[116])).
% 0.50/0.65 tff(118,plain,
% 0.50/0.65 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.50/0.65 inference(rewrite,[status(thm)],[])).
% 0.50/0.65 tff(119,plain,
% 0.50/0.65 (^[H: $i] : rewrite(((s2(H) | (~q2(b, H, b))) | (~s1(b))) <=> ((~s1(b)) | s2(H) | (~q2(b, H, b))))),
% 0.50/0.65 inference(bind,[status(th)],[])).
% 0.50/0.65 tff(120,plain,
% 0.50/0.65 (![H: $i] : ((s2(H) | (~q2(b, H, b))) | (~s1(b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.50/0.65 inference(quant_intro,[status(thm)],[119])).
% 0.50/0.65 tff(121,axiom,(![H: $i] : ((s2(H) | (~q2(b, H, b))) | (~s1(b)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_189')).
% 0.50/0.65 tff(122,plain,
% 0.50/0.65 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.50/0.65 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.50/0.65 tff(123,plain,
% 0.50/0.65 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.50/0.65 inference(modus_ponens,[status(thm)],[122, 118])).
% 0.50/0.65 tff(124,plain,(
% 0.50/0.65 ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.50/0.65 inference(skolemize,[status(sab)],[123])).
% 0.50/0.65 tff(125,plain,
% 0.50/0.65 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.50/0.65 inference(modus_ponens,[status(thm)],[124, 117])).
% 0.50/0.65 tff(126,plain,
% 0.50/0.65 (((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | ((~s1(b)) | s2(a) | (~q2(b, a, b)))) <=> ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | (~s1(b)) | s2(a) | (~q2(b, a, b)))),
% 0.50/0.65 inference(rewrite,[status(thm)],[])).
% 0.50/0.65 tff(127,plain,
% 0.50/0.65 ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | ((~s1(b)) | s2(a) | (~q2(b, a, b)))),
% 0.50/0.65 inference(quant_inst,[status(thm)],[])).
% 0.50/0.65 tff(128,plain,
% 0.50/0.65 ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | (~s1(b)) | s2(a) | (~q2(b, a, b))),
% 0.50/0.65 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.50/0.65 tff(129,plain,
% 0.50/0.65 (~q2(b, a, b)),
% 0.50/0.65 inference(unit_resolution,[status(thm)],[128, 125, 115, 22])).
% 0.50/0.65 tff(130,assumption,(~n1(a, b, a)), introduced(assumption)).
% 0.50/0.65 tff(131,plain,
% 0.50/0.65 (^[D: $i, E: $i] : refl(((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D)) <=> ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D)))),
% 0.50/0.65 inference(bind,[status(th)],[])).
% 0.50/0.65 tff(132,plain,
% 0.50/0.65 (![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D)) <=> ![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))),
% 0.50/0.65 inference(quant_intro,[status(thm)],[131])).
% 0.50/0.65 tff(133,plain,
% 0.50/0.65 (![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D)) <=> ![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))),
% 0.50/0.65 inference(rewrite,[status(thm)],[])).
% 0.50/0.65 tff(134,plain,
% 0.50/0.65 (^[D: $i, E: $i] : trans(monotonicity(trans(monotonicity(rewrite((n1(D, E, D) | (~s0(b))) <=> ((~s0(b)) | n1(D, E, D))), (((n1(D, E, D) | (~s0(b))) | (~l0(D))) <=> (((~s0(b)) | n1(D, E, D)) | (~l0(D))))), rewrite((((~s0(b)) | n1(D, E, D)) | (~l0(D))) <=> ((~l0(D)) | (~s0(b)) | n1(D, E, D))), (((n1(D, E, D) | (~s0(b))) | (~l0(D))) <=> ((~l0(D)) | (~s0(b)) | n1(D, E, D)))), ((((n1(D, E, D) | (~s0(b))) | (~l0(D))) | (~p0(b, E))) <=> (((~l0(D)) | (~s0(b)) | n1(D, E, D)) | (~p0(b, E))))), rewrite((((~l0(D)) | (~s0(b)) | n1(D, E, D)) | (~p0(b, E))) <=> ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))), ((((n1(D, E, D) | (~s0(b))) | (~l0(D))) | (~p0(b, E))) <=> ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))))),
% 0.50/0.65 inference(bind,[status(th)],[])).
% 0.50/0.65 tff(135,plain,
% 0.50/0.65 (![D: $i, E: $i] : (((n1(D, E, D) | (~s0(b))) | (~l0(D))) | (~p0(b, E))) <=> ![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))),
% 0.50/0.65 inference(quant_intro,[status(thm)],[134])).
% 0.50/0.65 tff(136,axiom,(![D: $i, E: $i] : (((n1(D, E, D) | (~s0(b))) | (~l0(D))) | (~p0(b, E)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_050')).
% 0.50/0.65 tff(137,plain,
% 0.50/0.65 (![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))),
% 0.50/0.65 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.50/0.65 tff(138,plain,
% 0.50/0.65 (![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))),
% 0.50/0.65 inference(modus_ponens,[status(thm)],[137, 133])).
% 0.50/0.65 tff(139,plain,(
% 0.50/0.65 ![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))),
% 0.50/0.65 inference(skolemize,[status(sab)],[138])).
% 0.50/0.65 tff(140,plain,
% 0.50/0.65 (![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))),
% 0.50/0.65 inference(modus_ponens,[status(thm)],[139, 132])).
% 0.50/0.65 tff(141,plain,
% 0.50/0.65 (s0(b) <=> s0(b)),
% 0.50/0.65 inference(rewrite,[status(thm)],[])).
% 0.50/0.65 tff(142,axiom,(s0(b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_5')).
% 0.50/0.65 tff(143,plain,
% 0.50/0.65 (s0(b)),
% 0.50/0.65 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.50/0.65 tff(144,plain,
% 0.50/0.65 (((~![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))) | ((~l0(a)) | (~s0(b)) | (~p0(b, b)) | n1(a, b, a))) <=> ((~![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))) | (~l0(a)) | (~s0(b)) | (~p0(b, b)) | n1(a, b, a))),
% 0.50/0.65 inference(rewrite,[status(thm)],[])).
% 0.50/0.65 tff(145,plain,
% 0.50/0.65 ((~![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))) | ((~l0(a)) | (~s0(b)) | (~p0(b, b)) | n1(a, b, a))),
% 0.50/0.65 inference(quant_inst,[status(thm)],[])).
% 0.50/0.65 tff(146,plain,
% 0.50/0.65 ((~![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))) | (~l0(a)) | (~s0(b)) | (~p0(b, b)) | n1(a, b, a)),
% 0.50/0.65 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.50/0.65 tff(147,plain,
% 0.50/0.65 ($false),
% 0.50/0.65 inference(unit_resolution,[status(thm)],[146, 143, 38, 140, 11, 130])).
% 0.50/0.65 tff(148,plain,(n1(a, b, a)), inference(lemma,lemma(discharge,[]))).
% 0.50/0.65 tff(149,plain,
% 0.50/0.65 (^[H: $i, G: $i] : refl(((~n0(H, G)) | l1(G, G)) <=> ((~n0(H, G)) | l1(G, G)))),
% 0.50/0.65 inference(bind,[status(th)],[])).
% 0.50/0.65 tff(150,plain,
% 0.50/0.65 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G)) <=> ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.50/0.65 inference(quant_intro,[status(thm)],[149])).
% 0.50/0.65 tff(151,plain,
% 0.50/0.65 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G)) <=> ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.50/0.65 inference(rewrite,[status(thm)],[])).
% 0.50/0.65 tff(152,plain,
% 0.50/0.65 (^[H: $i, G: $i] : rewrite((l1(G, G) | (~n0(H, G))) <=> ((~n0(H, G)) | l1(G, G)))),
% 0.50/0.65 inference(bind,[status(th)],[])).
% 0.50/0.65 tff(153,plain,
% 0.50/0.65 (![H: $i, G: $i] : (l1(G, G) | (~n0(H, G))) <=> ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.50/0.65 inference(quant_intro,[status(thm)],[152])).
% 0.50/0.65 tff(154,axiom,(![H: $i, G: $i] : (l1(G, G) | (~n0(H, G)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_002')).
% 0.50/0.65 tff(155,plain,
% 0.50/0.65 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.50/0.65 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.50/0.65 tff(156,plain,
% 0.50/0.65 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.50/0.65 inference(modus_ponens,[status(thm)],[155, 151])).
% 0.50/0.65 tff(157,plain,(
% 0.50/0.65 ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.50/0.65 inference(skolemize,[status(sab)],[156])).
% 0.50/0.65 tff(158,plain,
% 0.50/0.65 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.50/0.65 inference(modus_ponens,[status(thm)],[157, 150])).
% 0.50/0.65 tff(159,plain,
% 0.50/0.65 (n0(b, a) <=> n0(b, a)),
% 0.50/0.65 inference(rewrite,[status(thm)],[])).
% 0.50/0.65 tff(160,axiom,(n0(b, a)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_37')).
% 0.50/0.65 tff(161,plain,
% 0.50/0.65 (n0(b, a)),
% 0.50/0.65 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.50/0.65 tff(162,plain,
% 0.50/0.65 (((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | ((~n0(b, a)) | l1(a, a))) <=> ((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | (~n0(b, a)) | l1(a, a))),
% 0.50/0.65 inference(rewrite,[status(thm)],[])).
% 0.50/0.65 tff(163,plain,
% 0.50/0.65 ((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | ((~n0(b, a)) | l1(a, a))),
% 0.50/0.65 inference(quant_inst,[status(thm)],[])).
% 0.50/0.65 tff(164,plain,
% 0.50/0.65 ((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | (~n0(b, a)) | l1(a, a)),
% 0.50/0.65 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.50/0.65 tff(165,plain,
% 0.50/0.65 (l1(a, a)),
% 0.50/0.65 inference(unit_resolution,[status(thm)],[164, 161, 158])).
% 0.50/0.65 tff(166,plain,
% 0.50/0.65 (^[E: $i, F: $i, G: $i] : refl(((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F)) <=> ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F)))),
% 0.50/0.66 inference(bind,[status(th)],[])).
% 0.50/0.66 tff(167,plain,
% 0.50/0.66 (![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F)) <=> ![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 0.50/0.66 inference(quant_intro,[status(thm)],[166])).
% 0.50/0.66 tff(168,plain,
% 0.50/0.66 (![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F)) <=> ![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 0.50/0.66 inference(rewrite,[status(thm)],[])).
% 0.50/0.66 tff(169,plain,
% 0.50/0.66 (^[E: $i, F: $i, G: $i] : trans(monotonicity(trans(monotonicity(rewrite((n1(E, F, F) | (~l0(G))) <=> ((~l0(G)) | n1(E, F, F))), (((n1(E, F, F) | (~l0(G))) | (~l1(G, E))) <=> (((~l0(G)) | n1(E, F, F)) | (~l1(G, E))))), rewrite((((~l0(G)) | n1(E, F, F)) | (~l1(G, E))) <=> ((~l0(G)) | (~l1(G, E)) | n1(E, F, F))), (((n1(E, F, F) | (~l0(G))) | (~l1(G, E))) <=> ((~l0(G)) | (~l1(G, E)) | n1(E, F, F)))), ((((n1(E, F, F) | (~l0(G))) | (~l1(G, E))) | (~n1(E, F, E))) <=> (((~l0(G)) | (~l1(G, E)) | n1(E, F, F)) | (~n1(E, F, E))))), rewrite((((~l0(G)) | (~l1(G, E)) | n1(E, F, F)) | (~n1(E, F, E))) <=> ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))), ((((n1(E, F, F) | (~l0(G))) | (~l1(G, E))) | (~n1(E, F, E))) <=> ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))))),
% 0.50/0.66 inference(bind,[status(th)],[])).
% 0.50/0.66 tff(170,plain,
% 0.50/0.66 (![E: $i, F: $i, G: $i] : (((n1(E, F, F) | (~l0(G))) | (~l1(G, E))) | (~n1(E, F, E))) <=> ![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 0.50/0.66 inference(quant_intro,[status(thm)],[169])).
% 0.50/0.66 tff(171,axiom,(![E: $i, F: $i, G: $i] : (((n1(E, F, F) | (~l0(G))) | (~l1(G, E))) | (~n1(E, F, E)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_054')).
% 0.50/0.66 tff(172,plain,
% 0.50/0.66 (![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 0.50/0.66 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.50/0.66 tff(173,plain,
% 0.50/0.66 (![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 0.50/0.66 inference(modus_ponens,[status(thm)],[172, 168])).
% 0.50/0.66 tff(174,plain,(
% 0.50/0.66 ![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 0.50/0.66 inference(skolemize,[status(sab)],[173])).
% 0.50/0.66 tff(175,plain,
% 0.50/0.66 (![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 0.50/0.66 inference(modus_ponens,[status(thm)],[174, 167])).
% 0.50/0.66 tff(176,plain,
% 0.50/0.66 (((~![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))) | ((~l0(a)) | n1(a, b, b) | (~l1(a, a)) | (~n1(a, b, a)))) <=> ((~![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))) | (~l0(a)) | n1(a, b, b) | (~l1(a, a)) | (~n1(a, b, a)))),
% 0.50/0.66 inference(rewrite,[status(thm)],[])).
% 0.50/0.66 tff(177,plain,
% 0.50/0.66 (((~l0(a)) | (~n1(a, b, a)) | (~l1(a, a)) | n1(a, b, b)) <=> ((~l0(a)) | n1(a, b, b) | (~l1(a, a)) | (~n1(a, b, a)))),
% 0.50/0.66 inference(rewrite,[status(thm)],[])).
% 0.50/0.66 tff(178,plain,
% 0.50/0.66 (((~![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))) | ((~l0(a)) | (~n1(a, b, a)) | (~l1(a, a)) | n1(a, b, b))) <=> ((~![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))) | ((~l0(a)) | n1(a, b, b) | (~l1(a, a)) | (~n1(a, b, a))))),
% 0.50/0.66 inference(monotonicity,[status(thm)],[177])).
% 0.50/0.66 tff(179,plain,
% 0.50/0.66 (((~![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))) | ((~l0(a)) | (~n1(a, b, a)) | (~l1(a, a)) | n1(a, b, b))) <=> ((~![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))) | (~l0(a)) | n1(a, b, b) | (~l1(a, a)) | (~n1(a, b, a)))),
% 0.50/0.66 inference(transitivity,[status(thm)],[178, 176])).
% 0.50/0.66 tff(180,plain,
% 0.50/0.66 ((~![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))) | ((~l0(a)) | (~n1(a, b, a)) | (~l1(a, a)) | n1(a, b, b))),
% 0.50/0.66 inference(quant_inst,[status(thm)],[])).
% 0.50/0.66 tff(181,plain,
% 0.50/0.66 ((~![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))) | (~l0(a)) | n1(a, b, b) | (~l1(a, a)) | (~n1(a, b, a))),
% 0.50/0.66 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.50/0.66 tff(182,plain,
% 0.50/0.66 (n1(a, b, b)),
% 0.50/0.66 inference(unit_resolution,[status(thm)],[181, 38, 175, 165, 148])).
% 0.50/0.66 tff(183,plain,
% 0.50/0.66 (^[B: $i, C: $i] : refl(((~p0(C, B)) | p1(B, B, B)) <=> ((~p0(C, B)) | p1(B, B, B)))),
% 0.50/0.66 inference(bind,[status(th)],[])).
% 0.50/0.66 tff(184,plain,
% 0.50/0.66 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B)) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.50/0.66 inference(quant_intro,[status(thm)],[183])).
% 0.50/0.66 tff(185,plain,
% 0.50/0.66 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B)) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.50/0.66 inference(rewrite,[status(thm)],[])).
% 0.50/0.66 tff(186,plain,
% 0.50/0.66 (^[B: $i, C: $i] : rewrite((p1(B, B, B) | (~p0(C, B))) <=> ((~p0(C, B)) | p1(B, B, B)))),
% 0.50/0.66 inference(bind,[status(th)],[])).
% 0.50/0.66 tff(187,plain,
% 0.50/0.66 (![B: $i, C: $i] : (p1(B, B, B) | (~p0(C, B))) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.50/0.66 inference(quant_intro,[status(thm)],[186])).
% 0.50/0.66 tff(188,axiom,(![B: $i, C: $i] : (p1(B, B, B) | (~p0(C, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_085')).
% 0.50/0.66 tff(189,plain,
% 0.50/0.66 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.50/0.66 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.50/0.66 tff(190,plain,
% 0.50/0.66 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.50/0.66 inference(modus_ponens,[status(thm)],[189, 185])).
% 0.50/0.66 tff(191,plain,(
% 0.50/0.66 ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.50/0.66 inference(skolemize,[status(sab)],[190])).
% 0.50/0.66 tff(192,plain,
% 0.50/0.66 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.50/0.66 inference(modus_ponens,[status(thm)],[191, 184])).
% 0.50/0.66 tff(193,plain,
% 0.50/0.66 (p0(c, b) <=> p0(c, b)),
% 0.50/0.66 inference(rewrite,[status(thm)],[])).
% 0.50/0.66 tff(194,axiom,(p0(c, b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_18')).
% 0.50/0.66 tff(195,plain,
% 0.50/0.66 (p0(c, b)),
% 0.50/0.66 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.50/0.66 tff(196,plain,
% 0.50/0.66 (((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | ((~p0(c, b)) | p1(b, b, b))) <=> ((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | (~p0(c, b)) | p1(b, b, b))),
% 0.50/0.66 inference(rewrite,[status(thm)],[])).
% 0.50/0.66 tff(197,plain,
% 0.50/0.66 ((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | ((~p0(c, b)) | p1(b, b, b))),
% 0.50/0.66 inference(quant_inst,[status(thm)],[])).
% 0.50/0.66 tff(198,plain,
% 0.50/0.66 ((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | (~p0(c, b)) | p1(b, b, b)),
% 0.50/0.66 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.50/0.66 tff(199,plain,
% 0.50/0.66 (p1(b, b, b)),
% 0.50/0.66 inference(unit_resolution,[status(thm)],[198, 195, 192])).
% 0.50/0.66 tff(200,plain,
% 0.50/0.66 (^[H: $i, F: $i, G: $i] : refl(((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F)) <=> ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F)))),
% 0.50/0.66 inference(bind,[status(th)],[])).
% 0.50/0.66 tff(201,plain,
% 0.50/0.66 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F)) <=> ![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 0.50/0.66 inference(quant_intro,[status(thm)],[200])).
% 0.50/0.66 tff(202,plain,
% 0.50/0.66 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F)) <=> ![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 0.50/0.66 inference(rewrite,[status(thm)],[])).
% 0.50/0.66 tff(203,plain,
% 0.50/0.66 (^[H: $i, F: $i, G: $i] : trans(monotonicity(trans(monotonicity(rewrite((q2(F, G, F) | (~p1(F, F, H))) <=> ((~p1(F, F, H)) | q2(F, G, F))), (((q2(F, G, F) | (~p1(F, F, H))) | (~n1(G, F, H))) <=> (((~p1(F, F, H)) | q2(F, G, F)) | (~n1(G, F, H))))), rewrite((((~p1(F, F, H)) | q2(F, G, F)) | (~n1(G, F, H))) <=> ((~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))), (((q2(F, G, F) | (~p1(F, F, H))) | (~n1(G, F, H))) <=> ((~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F)))), ((((q2(F, G, F) | (~p1(F, F, H))) | (~n1(G, F, H))) | (~q2(G, H, F))) <=> (((~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F)) | (~q2(G, H, F))))), rewrite((((~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F)) | (~q2(G, H, F))) <=> ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))), ((((q2(F, G, F) | (~p1(F, F, H))) | (~n1(G, F, H))) | (~q2(G, H, F))) <=> ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))))),
% 0.50/0.66 inference(bind,[status(th)],[])).
% 0.50/0.66 tff(204,plain,
% 0.50/0.66 (![H: $i, F: $i, G: $i] : (((q2(F, G, F) | (~p1(F, F, H))) | (~n1(G, F, H))) | (~q2(G, H, F))) <=> ![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 0.50/0.66 inference(quant_intro,[status(thm)],[203])).
% 0.50/0.66 tff(205,axiom,(![H: $i, F: $i, G: $i] : (((q2(F, G, F) | (~p1(F, F, H))) | (~n1(G, F, H))) | (~q2(G, H, F)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_182')).
% 0.50/0.66 tff(206,plain,
% 0.50/0.66 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 0.50/0.66 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.50/0.66 tff(207,plain,
% 0.50/0.66 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 0.50/0.66 inference(modus_ponens,[status(thm)],[206, 202])).
% 0.50/0.66 tff(208,plain,(
% 0.50/0.66 ![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 0.50/0.66 inference(skolemize,[status(sab)],[207])).
% 0.50/0.66 tff(209,plain,
% 0.50/0.66 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 0.50/0.66 inference(modus_ponens,[status(thm)],[208, 201])).
% 0.50/0.66 tff(210,plain,
% 0.50/0.66 (((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | ((~p1(b, b, b)) | q2(b, a, b) | (~q2(a, b, b)) | (~n1(a, b, b)))) <=> ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | (~p1(b, b, b)) | q2(b, a, b) | (~q2(a, b, b)) | (~n1(a, b, b)))),
% 0.50/0.66 inference(rewrite,[status(thm)],[])).
% 0.50/0.66 tff(211,plain,
% 0.50/0.66 (((~q2(a, b, b)) | (~n1(a, b, b)) | (~p1(b, b, b)) | q2(b, a, b)) <=> ((~p1(b, b, b)) | q2(b, a, b) | (~q2(a, b, b)) | (~n1(a, b, b)))),
% 0.50/0.66 inference(rewrite,[status(thm)],[])).
% 0.50/0.66 tff(212,plain,
% 0.50/0.66 (((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | ((~q2(a, b, b)) | (~n1(a, b, b)) | (~p1(b, b, b)) | q2(b, a, b))) <=> ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | ((~p1(b, b, b)) | q2(b, a, b) | (~q2(a, b, b)) | (~n1(a, b, b))))),
% 0.50/0.66 inference(monotonicity,[status(thm)],[211])).
% 0.50/0.66 tff(213,plain,
% 0.50/0.66 (((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | ((~q2(a, b, b)) | (~n1(a, b, b)) | (~p1(b, b, b)) | q2(b, a, b))) <=> ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | (~p1(b, b, b)) | q2(b, a, b) | (~q2(a, b, b)) | (~n1(a, b, b)))),
% 0.50/0.66 inference(transitivity,[status(thm)],[212, 210])).
% 0.50/0.66 tff(214,plain,
% 0.50/0.66 ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | ((~q2(a, b, b)) | (~n1(a, b, b)) | (~p1(b, b, b)) | q2(b, a, b))),
% 0.50/0.66 inference(quant_inst,[status(thm)],[])).
% 0.50/0.66 tff(215,plain,
% 0.50/0.66 ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | (~p1(b, b, b)) | q2(b, a, b) | (~q2(a, b, b)) | (~n1(a, b, b))),
% 0.50/0.66 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.50/0.66 tff(216,plain,
% 0.50/0.66 (~q2(a, b, b)),
% 0.50/0.66 inference(unit_resolution,[status(thm)],[215, 209, 199, 182, 129])).
% 0.50/0.66 tff(217,plain,
% 0.50/0.66 (^[E: $i, F: $i] : refl(((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F)) <=> ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F)))),
% 0.50/0.66 inference(bind,[status(th)],[])).
% 0.50/0.66 tff(218,plain,
% 0.50/0.66 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F)) <=> ![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 0.50/0.66 inference(quant_intro,[status(thm)],[217])).
% 0.50/0.66 tff(219,plain,
% 0.50/0.66 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F)) <=> ![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 0.50/0.66 inference(rewrite,[status(thm)],[])).
% 0.50/0.66 tff(220,plain,
% 0.50/0.66 (^[E: $i, F: $i] : trans(monotonicity(rewrite((q2(E, F, F) | (~k0(F))) <=> ((~k0(F)) | q2(E, F, F))), (((q2(E, F, F) | (~k0(F))) | (~p1(E, E, E))) <=> (((~k0(F)) | q2(E, F, F)) | (~p1(E, E, E))))), rewrite((((~k0(F)) | q2(E, F, F)) | (~p1(E, E, E))) <=> ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))), (((q2(E, F, F) | (~k0(F))) | (~p1(E, E, E))) <=> ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))))),
% 0.50/0.67 inference(bind,[status(th)],[])).
% 0.50/0.67 tff(221,plain,
% 0.50/0.67 (![E: $i, F: $i] : ((q2(E, F, F) | (~k0(F))) | (~p1(E, E, E))) <=> ![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 0.50/0.67 inference(quant_intro,[status(thm)],[220])).
% 0.50/0.67 tff(222,axiom,(![E: $i, F: $i] : ((q2(E, F, F) | (~k0(F))) | (~p1(E, E, E)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_177')).
% 0.50/0.67 tff(223,plain,
% 0.50/0.67 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.50/0.67 tff(224,plain,
% 0.50/0.67 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[223, 219])).
% 0.50/0.67 tff(225,plain,(
% 0.50/0.67 ![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 0.50/0.67 inference(skolemize,[status(sab)],[224])).
% 0.50/0.67 tff(226,plain,
% 0.50/0.67 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[225, 218])).
% 0.50/0.67 tff(227,plain,
% 0.50/0.67 (k0(b) <=> k0(b)),
% 0.50/0.67 inference(rewrite,[status(thm)],[])).
% 0.50/0.67 tff(228,axiom,(k0(b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_32')).
% 0.50/0.67 tff(229,plain,
% 0.50/0.67 (k0(b)),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[228, 227])).
% 0.50/0.67 tff(230,plain,
% 0.50/0.67 (((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | ((~k0(b)) | (~p1(a, a, a)) | q2(a, b, b))) <=> ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | (~k0(b)) | (~p1(a, a, a)) | q2(a, b, b))),
% 0.50/0.67 inference(rewrite,[status(thm)],[])).
% 0.50/0.67 tff(231,plain,
% 0.50/0.67 ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | ((~k0(b)) | (~p1(a, a, a)) | q2(a, b, b))),
% 0.50/0.67 inference(quant_inst,[status(thm)],[])).
% 0.50/0.67 tff(232,plain,
% 0.50/0.67 ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | (~k0(b)) | (~p1(a, a, a)) | q2(a, b, b)),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.50/0.67 tff(233,plain,
% 0.50/0.67 ($false),
% 0.50/0.67 inference(unit_resolution,[status(thm)],[232, 229, 91, 226, 216])).
% 0.50/0.67 % SZS output end Proof
% 0.50/0.67 % E exiting
%------------------------------------------------------------------------------